Computer Science 1 Ah

Transcription

1 UNIVERSITY OF EDINBURGH course CS0077 FACULTY OF SCIENCE AND ENGINEERING DIVISION OF INFORMATICS SCHOOL OF COMPUTER SCIENCE Computer Science 1 Ah Degree Examination Date: Saturday 25th May 2002 Time: 09:30 11:00 (one and a half hours) Place: Adam House Room: Ground Floor Board of examiners Chair: D.K. Arvind External Examiner: R. Dyckhoff Instructions to candidates 1. Check that the question paper contains pages 1 11 after this cover page. If it does not, inform the invigilator. 2. You should attempt as many questions as possible. 3. The questions in this paper vary widely in difficulty. During your first pass through the paper, you are advised not to dwell on questions to which the answer is not readily apparent. 4. Write your answer to each question in the box or table provided. If you wish to write more in answer to a question, continue on the blank page opposite, indicating that you have done so. 5. Please write legible and concise answers. 6. The marks allocated to each part of a question are indicated in the margin. There are 100 marks in total.

2 Question 1 (a) For each of the following kinds of data, give the most appropriate type or class for representing values in Java. Take care with capitalization; remember that Java identifiers are case-sensitive. i. A sequence of characters representing a line of text that was filled in on a web page form. ii. The CO 2 emissions of a car, measured in kg/km, accurate to three decimal places (typical emissions figures range from 120g/km 250g/km). iii. The sequence of airports visited using an unlimited around-the-world air ticket. Your answer should work for any choice of class used to represent an airport. iv. The representation of a pixel greyscale image, where a grey pixel is represented as an 8-bit number. v. The representation of a pixel image mask, which defines a portion of an image (each pixel may be in the mask or not). vi. The representation of a pixel colour image, using a class Colour whose objects represent colours. (b) In programming, we often examine a value of a type in a particular way, according to the type of the value. In Java, particular control structures are associated with different types of value and the way we might examine them. Complete the statements below which illustrate this association, showing appropriate control structures for processing values of the given type. [4 marks] I would use a for-loop to process a value of type int[]. i. I would use a to process a value of type boolean. ii. I would use a to process a value of type StreamTokenizer. iii. I would use a with an to process a value of type Vector.

3 Question 2 (a) Consider the tree shown below. n 0 n 1 n 2 n 3 n 4 n 5 n 6 n 7 i. How many leaves does this tree have? n 8 n 9 ii. If the nodes of the tree were rearranged to make a maximally-tall binary tree, how many leaves would the rearranged tree have? iii. Assuming there is an ordering on subtrees from left to right, show the order that the nodes would be visited in a pre-order traversal. [2 marks] (b) Complete the following method for counting the number of nodes in a binary tree (BinTree is a class with two BinTree fields left and right). private static int size(bintree tree) { if (tree!= ) { return 1 + size( ) + size( ); else { [2 marks] (c) Give the definition for an instance method size in the BinTree class, which uses the above static size method to calculate the size of a non-empty tree object. [2 marks]

4 Question 3 (a) Place a tick in the box to indicate whether the following statements about Java exceptions are true or false. [5 marks] true false Exception is a class of the Java language. It is possible to invoke methods on exceptions. It is possible to exit a loop in the middle by throwing an exception. It is possible to enter a loop in the middle by throwing an exception. All exceptions a method can throw must be specified with throws. (b) Complete the following template to produce a Java program which reads all of the Student objects from an object input stream and then closes the stream at the end. import java.io.*; class StudentReport { public static void main(string[] args) { try { /* Read the file of student records */ String name = "Students.dat"; FileInputStream file = ObjectInputStream in = while (true) { try { ; ; Student s = ; System.out.println(s); catch (EOFException e) { System.out.println("End of report"); catch (Exception e) { e.printstacktrace();

5 Question 4 (a) What operations take place when a Java method with parameters is invoked? [3 marks] (b) Consider the following Java program. What output does it produce? [2 marks] class Hello { static void copy (String s) { s = s + s; public static void main (String[] args) { String hello = "Hello"; System.out.println(hello); copy(hello); copy(hello); System.out.println(hello); (c) What does it mean for a Java method to be marked as static? [3 marks] (d) Consider the following Java program fragment. public class Outer { public static class Inner { public static int four() { return 4; How would the method four() above be invoked from another Java class? [2 marks]

6 Question 5 (a) Construct finite state machines with the input alphabet {0, 1 that: i. Accept exactly those strings that include two occurrences of the pattern 010. Note that the occurrences could be overlapping. [3 marks] ii. Accept those strings not containing an occurrence of the string [2 marks] (b) Can a finite state machine accept exactly the following sets of strings? Place a tick in the box if so and a cross otherwise. i. all strings s of 0s and 1s where in any prefix r of s the difference between the number of 0s and the number of 1s lies between -3 and +3.. ii. all strings of 0s and 1s where the difference between the total number of 0s and the number of 1s lies between -3 and +3. (c) Write a regular expression that describes all strings containing just 0s and 1s where the number of 0s is odd or the number of 1s is even. [3 marks]

7 Question 6 Consider the following brief description of the accident and emergency service at a hospital: Patients arrive at the emergency service. On their arrival they are registered as a case to be dealt with by the service, they are first assessed (a process called triage), their details are taken (name, address, doctor) and allocated to a particular group. The triage groups are: immediate, urgent and non-urgent. Each patient is then treated in the emergency unit and after treatment the case is closed. On the closing of the case the time of closing is compared with the time the case was created to help in the calculation of waiting time statistics for different triage groups. (a) Use the techniques of identifying noun phrases to identify the classes one would need to provide a model of this system. List the names of the classes you think you would require. [5 marks] (b) Show how you would implement these classes in Java. Give the class definitions with the main attributes for each class. You do not need to identify any methods in the classes you define. [5 marks]

8 Question 7 (a) Explain informally how the selection sort algorithm for sorting the elements of an array works. [3 marks] (b) What is the worst case run time (as a big-oh expression in terms of n) for sorting n elements with selection sort? (c) Show how selection sort sorts the following array by writing down the contents of the array each time an element is moved [6 marks]

9 Question 8 A simple hot drink vending machine supplies either tea or coffee when a user inserts money, then presses an appropriate button. For simplicity, the machine only accepts one type of coin. It can supply tea if at least one coin has been inserted and can supply coffee if at least two coins have been inserted. No more than three coins worth of credit can be outstanding at any time. The input actions of the machine are: coin The user inserts a coin. teaask The user presses the tea button and expects to get a cup of tea if enough money has been inserted. coffeeask The user presses the coffee button and expects to get a cup of coffee if enough money has been inserted. refund The user presses the refund button and expects all unspent inserted money to be returned. The output actions are: teasupply Supply a cup of tea to the user. coffeesupply Supply a cup of coffee to the user. return Return all unspent money inserted. (a) Draw a finite state machine for this system. Be careful to take account of all possible sequences of input actions. [7 marks] (b) Write down a sequence of input actions that causes every state in your machine to be visited. [3 marks]

10 Question 9 (a) i. Draw a truth table for the logical expression ( A B) (B A), including columns for the intermediate sub-expressions A, A B, and B A. ii. Is it a tautology? Give a one line explanation of your answer. [3 marks] (b) Using the algebraic laws of boolean logic, simplify the logical expression A ( A B), writing each step of the simplification on a separate line. [2 marks] (c) Assume variable i has initial value 0. What is the value of i after evaluating each of the following boolean expressions in Java? i. i++ == 0 & i++ == 1 ii. i++ == 1 && i++ == 0 iii. i++ == 0 && i++ == 1 iv. i++ == 1 i++ == 0 [4 marks]

11 Question 10 (a) For each of the following recursive methods, enter Y in the box if the method f terminates if given the value 5 as argument. Otherwise enter N. i. static int f(int i) { return f(i - 1) * f(i - 1); ii. static int f(int i) { if (i == 0) {return 1; else {return f(i - 1) * f(i - 1); iii. static int f(int i) { if (i == 0) {return 1; else {return f(i - 1) * f(i - 2); (b) What is printed out by the recursive method: static void g(int i) { System.out.print(i + " "); if (i == 1) {return; if (i%2 == 0) {g(i/2);return; else {g(3*i+1);return; when invoked with the value 5? [2 marks] [ Question continues on next page ]

12 (c) Java defines a Stack class including the constructor and methods: public Stack(); public void push(object o); public Object pop(); public boolean empty(); Using these, complete the definition of the static method stackcopy below. Your stackcopy method should create a fresh copy of the Stack object argument with elements in the same order. Further, it should leave the original stack in its initial state, though it will need to change the original stack during its execution. As necessary, use extra Stack objects for temporary storage. public class StackUtils { public static Stack stackcopy(stack s) { [5 marks]